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On differential equations in normal form

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References

  1. Arms, J., Cushman, R., Gotay, M.: A universal reduction procedure for Hamiltonian group actions. Preprint #591, University of Utrecht (1989)

  2. Arnold, V.I., Anosov, D.V. (eds.): Dynamical systems. I. Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  3. Bruno, A.D.: Local methods in nonlinear differential equations. Berlin Heidelberg New York: Springer 1989

    Google Scholar 

  4. Bruno (Brjuno), A.D.: Analytical form of differential equations. I. Trans. Mosc. Math. Soc.25, 131–288 (1971)

    Google Scholar 

  5. Bruno (Brjuno), A.D.: Analytical form of differential equations. II. Trans. Mosc. Math. Soc.26, 199–239 (1972)

    Google Scholar 

  6. Cushman, R., Deprit, A., Mosak, R.: Normal form and representation theory. J. Math. Phys.24, (8), 2102–2117 (1983)

    Google Scholar 

  7. Cushman, R., Rod, D.: Reduction of the semisimple 1∶1-resonance. Physica D6, 105–112 (1982)

    Google Scholar 

  8. Cushman, R., Sanders, J.: A survey of invariant theory applied to normal forms of vector fields with nilpotent linear part. In: Stanton, D. (ed.) Invariant theory and tableaux. (IMA Vol. Math. Appl. vol. 19, pp. 82–106) New York: Springer 1990

    Google Scholar 

  9. Cushman, R., Sjamaar, R.: On singular reduction of Hamiltonian spaces. Preprint #623, University of Utrecht (1990)

  10. Guckenheimer, J., Holmes, P.: Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  11. Humphreys, J.: Introduction to Lie algebras and representation theory. Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  12. Kummer, M.: On resonant Hamiltonian systems with finitely many degrees of freedom. (Lect. Notes Phys., vol. 252, pp. 19–31) Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  13. Kunz, E.: Introduction to commutative algebra and algebraic geometry. Boston Basel Stuttgart: Birkhäuser 1985

    Google Scholar 

  14. Olver, P.J.: Applications of Lie groups to differential equations. Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  15. Takens, F.: Singularities of vector fields. Publ. Math., Inst. Hautes Étud. Sci.43, 47–100 (1974)

    Google Scholar 

  16. van der Meer, J.: The Hamiltonian Hopf bifurcation. (Lect. Notes Math., vol. 1160) Berlin Heidelberg New York: Springer 1985

    Google Scholar 

  17. Walcher, S.: Über polynomiale, insbesondere Riccatische, Differentialgleichungen mit Fundamentallösungen. Math. Ann.275, 269–280 (1986)

    Google Scholar 

  18. Weitzenböck, W.: Über die Invarianten von linearen Gruppen. Acta Math.58, 231–293 (1932)

    Google Scholar 

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Walcher, S. On differential equations in normal form. Math. Ann. 291, 293–314 (1991). https://doi.org/10.1007/BF01445209

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